Active matter systems are attracting great interest in physics, as non-equilibrium systems with rich emergent behaviour. Some of their features can be captured by multi-species exclusion processes, whose hydrodynamic limits can be derived exactly. I will discuss the behaviour of several such models, including their hydrodynamic limits [1,2], and large (rare) fluctuations [3].

[1] J. Mason, C. Erignoux, R. L. Jack, and M. Bruna, Proc. Roy. Soc. A 479, 2279 (2023).
[2] J. Mason, R. L. Jack, and M. Bruna, arXiv:2408.03932.
[3] T. Agranov, M. E. Cates and R. L. Jack, J. Stat. Mech. (2022), 123201.